Date: Tue, 10 Dec 1996 16:51:45 GMT
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<title>CSE 321 Assignment #6</title>
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<h1>CSE 321 Assignment #6<br>Autumn 1996</h1>
<h3>Due: Friday, November 15, 1996.
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Reading Assignment: Read sections 4.4, 4.5, and 6.1 of the text.
The following problems are from the Third Edition of the text.
 
<p> Practice Problems: page 259, Problem 25; page 280, Problem 13
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<p> Problems: 
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<p><li> page 258, Problem 16.
<p><li> page 259, Problem 26.
<p><li> Use the binomial theorem to show that 
<p> C(n,0) + 2 C(n,1) + 4 C(n,2) + ...+ 2^k C(n,k) + ... + 2^n C(n,n) = 3^n.
<p><li> page 267, Problem 22.
<p><li> page 267, Problem 32.  Justify your answer.
<p><li> What is the conditional probability that at least 3 heads appear out
of 5 flips of a fair coin given that the first flip was tails?
<p><li> page 280, Problem 16.
<p><li> page 281, Problem 18.
<p><li> (Bonus) The Monty Hall Problem:  On the TV show ``Let's make a Deal''
a contestant would be shown 3 doors and allowed to choose one of the 3 doors.
Behind these 3 doors would be 2 booby prizes and 1 good prize.
Before the chosen door was opened Monty Hall would then open one of the
other two doors to display a booby prize and give the contestant a chance
to change his/her choice.  
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<li> Compute the original probability that the chosen door concealed a good
prize.
<li> Compute the conditional probability that the 3rd door (not the chosen
one nor the opened one) conceals a good prize.
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Based on these calculations what should the contestant do?
<p><li> (Bonus) Compute the conditional probability that a player has two aces
in a Poker hand conditioned on the fact that he has one ace.
Compute the conditional probability that a player has two aces in a Poker
hand conditioned on the fact that he has the Ace of Hearts.
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